Mean-variance analysis of the newsvendor problem with price-dependent, isoelastic demand

We present a mean-variance analysis of the single-product, single-period newsvendor problem with two decision variables, price and stock quantity. The demand is price-dependent, multiplicative, and isoelastic, and the product sold is price-elastic. The main goal of this paper is to completely characterize a framework where most risk sensitivities can be studied and find conditions under which the unimodality of this mean-variance performance measure is guaranteed. We aim at presenting these conditions in terms of a metric that can capture managerial attention. To this end we use the lost sales rate (LSR) elasticity, as it relates directly to the retailer's level of service. The main contribution of this paper is that, with very few and mild assumptions, we complement currently existing results for the uniqueness of the solution in the presence of price-inelastic products by extending the applicability of the LSR elasticity to the problem with price-elastic goods and assess its unimodality when the decision maker is risk-neutral or risk-sensitive. Finally, we compare the results under this model with others previously obtained for additive demand models, and we emphasize the reasons that make it difficult to attain similar results with an isoelastic demand model.